Problem 1 Consider an LC circuit. Assume that at time t = 0, the capacitor has charge Q. C HH L 0000 (a) Using Kirchoff's Laws, write down a differential equation for the charge q in the circuit. (b) Write the charge q(t) and current i(t) which satisfies the differential equation obtained in (a) and the condition that q(t = 0) = Q and i(t = 0) = 0. (c) Find the energy stored in the capacitor as a function of time. (d) Find the energy stored in the inductor as a function of time. (e) Demonstrate that the total energy in the circuit is conserved.